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GED Math : Solving for the Variable

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #61 : Solving For The Variable

Solve: 7x-6 = 15

Possible Answers:

$\frac{11}{7}$

$\frac{9}{7}$

$\frac{7}{9}$

$\frac{23}{7}$

Correct answer:

Explanation:

Add six on both sides.

7x-6 +6= 15+6

7x=21

Divide by 7 on both sides.

$\frac{7x}{7}=\frac{21}{7}$

The answer is:

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Example Question #62 : Solving For The Variable

Solve: $\frac{1}{4}x= 2x-3$

Possible Answers:

$-\frac{3}{8}$

$-\frac{4}{3}$

$\frac{12}{7}$

$-\frac{1}{3}$

$-\frac{8}{3}$

Correct answer:

$\frac{12}{7}$

Explanation:

Multiply by four on both sides to eliminate the fraction.

$\frac{1}{4}x\cdot 4= 4(2x-3)$

Simplify both sides.

x = 8x-12`

Subtract from both sides.

x-8x = 8x-12`-8x

-7x=-12

Divide by negative seven on both sides.

$\frac{-7x}{-7}=\frac{-12}{-7}$

The answer is: $\frac{12}{7}$

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Example Question #63 : Solving For The Variable

Solve for the variable: 5x-18 = 32

Possible Answers:

$\frac{14}{5}$

$\frac{24}{5}$

Correct answer:

Explanation:

Add 18 on both sides.

5x-18 +18= 32+18

5x= 50

Divide by 5 on both sides.

$\frac{5x}{5}=\frac{ 50}{5}$

The answer is:

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Example Question #61 : Solving For The Variable

Solve: $\frac{2}{5}x = \frac{1}{3}$

Possible Answers:

$\frac{9}{5}$

$\frac{6}{5}$

$\frac{2}{15}$

$\frac{5}{6}$

Correct answer:

$\frac{5}{6}$

Explanation:

To isolate the x-variable, multiply both sides by the reciprocal of the fraction in front of the x-variable.

$\frac{2}{5}x\cdot \frac{5}{2} = \frac{1}{3}\cdot \frac{5}{2}$

Simplify both sides.

The answer is: $\frac{5}{6}$

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Example Question #65 : Solving For The Variable

Solve for the variable: $2x-3 = \frac{1}{7}$

Possible Answers:

$\frac{11}{7}$

$\frac{3}{14}$

$\frac{22}{7}$

$\frac{7}{3}$

Correct answer:

$\frac{11}{7}$

Explanation:

Multiply by seven on both sides.

$7(2x-3) = \frac{1}{7}\cdot7$

14x-21 = 1

Add 21 on both sides.

14x-21 +21= 1+21

14x=22

Divide by 14 on both sides.

$\frac{14x}{14}=\frac{22}{14}$

Reduce both fractions.

The answer is: $\frac{11}{7}$

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Example Question #65 : Solving For The Variable

Solve for : 3y-7 = 4y

Possible Answers:

$-\frac{7}{12}$

Correct answer:

Explanation:

Subtract from both sides.

3y-7-3y = 4y-3y

Simplify both sides.

-7 =y

The answer is:

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Example Question #66 : Solving For The Variable

Solve for : $\frac{1}{2}x +\frac{7}{3} = \frac{8}{3}$

Possible Answers:

$\frac{1}{6}$

$\textup{The answer is not given.}$

$\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

Multiply both sides by the least common denominator to cancel out the fractions.

$6(\frac{1}{2}x +\frac{7}{3}) = \frac{8}{3}\cdot6$

3x+14 = 16

Subtract 14 on both sides.

3x+14 -14= 16-14

3x=2

Divide by 3 on both sides.

$\frac{3x}{3}=\frac{2}{3}$

The answer is: $\frac{2}{3}$

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Example Question #68 : Solving For The Variable

Given the following equation, find the value of b when w=-3

$b-2=\frac{5w+12}{3}+4$

Possible Answers:

Correct answer:

Explanation:

Given the following equation, find the value of b when w=-3

$b-2=\frac{5w+12}{3}+4$

This may look a little messy up front, but don't worry, it's not overly complicated.

All we need to do is plug in -3 for w and solve for b.

Let's begin:

$b-2=\frac{5(-3)+12}{3}+4$

$b-2=\frac{-15+12}{3}+4$

Now add our numbers:

$b-2=\frac{-3}{3}+4$

Now we can simplify our fraction to get:

b-2=-1+4

From her on out it is just subtraction and addition:

b-2=3

b=3+2=5

So our answer is 5

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Example Question #67 : Solving For The Variable

Solve for .

$\sqrt{3x+4}-2=6$

Possible Answers:

Correct answer:

Explanation:

$\sqrt{3x+4}-2=6$

Start by adding to both sides.

$\sqrt{3x+4}=8$

Next, square both sides to get rid of the square root.

3x+4=64

Subtract from both sides.

3x=60

Finally, divide both sides by .

x=20

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Example Question #61 : Solving For The Variable

Solve for :

$\sqrt{3x-1}+5=9$

Possible Answers:

$\frac{17}{3}$

$\frac{3}{17}$

Correct answer:

$\frac{17}{3}$

Explanation:

$\sqrt{3x-1}+5=9$

Start by subtracting from both sides.

$\sqrt{3x-1}=4$

Now, square both sides of the equation to get rid of the square root.

3x-1=16

Add to both sides.

3x=17

Divide both sides by .

$x=\frac{17}{3}$

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All GED Math Resources

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GED Math : Solving for the Variable

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #61 : Solving For The Variable

Example Question #62 : Solving For The Variable

Example Question #63 : Solving For The Variable

Example Question #61 : Solving For The Variable

Example Question #65 : Solving For The Variable

Example Question #65 : Solving For The Variable

Example Question #66 : Solving For The Variable

Example Question #68 : Solving For The Variable

Example Question #67 : Solving For The Variable

Example Question #61 : Solving For The Variable

All GED Math Resources

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